On domain of Poisson operators and factorization for divergence form elliptic operators

Yasunori Maekawa, Hideyuki Miura

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We consider second order uniformly elliptic operators of divergence form in Rd + 1 whose coefficients are independent of one variable. For such a class of operators we establish a factorization into a product of first order operators related with Poisson operators and Dirichlet–Neumann maps. Consequently, we obtain a solution formula for the inhomogeneous elliptic boundary value problem in the half space, which is useful to show the existence of solutions in a wider class of inhomogeneous data. We also establish L2 solvability of boundary value problems for a new class of the elliptic operators.

Original languageEnglish
Pages (from-to)459-512
Number of pages54
Journalmanuscripta mathematica
Volume152
Issue number3-4
DOIs
Publication statusPublished - 2017 Mar 1

Keywords

  • 35J15
  • 35J25

ASJC Scopus subject areas

  • Mathematics(all)

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